1. Field of the Invention
This invention relates to the field of estimating in-situ permeability of the reservoir rocks. More specifically, the invention is related to a method of determining the dynamic elastic nonlinear interaction between the Fast Compressional Seismic Wave that travels through the rock matrix and a liquid/solid coupled slower Compressional Seismic Wave that travels through the interconnected fluid-filled pores. The presence of this slower Compressional Wave in a hydrocarbon reservoir formation is a strong indicator of the formation""s bulk permeability. In this invention, the slower Compressional Wave that is generated, due to the solid/liquid coupling as the Fast Compressional Wave propagates through a permeable rock formation, is identified as xe2x80x9cDrag-Wave.xe2x80x9d This Drag-Wave travels at the pore fluid compressional velocity but over a longer distance along the tortuous path of the interconnected pores. The elastic nonlinear interaction between the Fast Compressional Wave and the Drag-Wave, as they propagate through a reservoir formation, generates summed and differenced frequencies of the two waves. From this information the Drag-Wave velocity can be calculated. From the Drag-Wave velocity we can calculate the bulk tortuosity of the formation. Permeability that is dependent on the pore size and the tortuosity of the pores can be determined, once the tortuosity is known.
2. Description of the Related Art
Permeability is often the most important factor in influencing the commercial viability of a hydrocarbon reservoir. So far, permeability cannot be measured directly in-situ in reservoir formations. Downhole tools that measure permeability in a borehole quite often provide ambiguous results, and these results are confined to the immediate vicinity of the wellbore. Measurement or estimation of permeability in carbonate reservoir rocks is even more difficult, since carbonates are more heterogeneous compared to sandstones.
A new seismic method that can estimate the bulk permeability of the reservoir formations between the wells will be extremely useful for implementing an efficient production program for a hydrocarbon-producing field that will optimize the economics of the hydrocarbon recovery.
Biot (1956) proposed a comprehensive theory that explained many important features of the seismic wave propagation in fluid-saturated porous media. One of the important contributions of his theory is the prediction of a Slow Compressional Wave with a speed lower than that of the rock matrix or the pore fluid. The Slow-Wave involves a coupled motion between the fluid and the solid frame. The Slow-Wave""s velocity and attenuation depend on the morphology of the pore space and the pore interconnections, which also determine the fluid transport properties such as permeability. The detection of the presence of the Slow-Wave in a reservoir formation between two wells is a strong indicator that the formation is permeable.
The Slow-Wave has been successfully measured under laboratory conditions using samples of glass beads and sand stone samples from typical reservoir formations (Berea and Massillon). Considerable effort has been made to detect the Slow-Wave in in-situ sedimentary rocks. So far this effort has not been very successful.
Since information related to in-situ rock permeability of the reservoir formations is extremely important for developing an accurate reservoir simulation model of its flow units, a new method of estimating the permeability of in-situ reservoir formations has been developed. In this invention, we determine the existence and the properties of the Slow-Wave for estimating the bulk tortuosity and permeability of the in-situ reservoir formations.
This invention introduces a new method of mapping reservoir flow units by identifying the in-situ permeability of the reservoir formations between the existing wells. To economically produce hydrocarbons from a reservoir, the reservoir rocks have to be porous so that the fluids can be stored in the pores. The pores have to be connected so that the reservoir fluids can flow between the pores. The capacity of transmitting a fluid in a rock depends on the size and shape of the pores, size and shape of the interconnections and their extent, and is known as permeability.
When a pressure wave travels through a rock, the rock matrix and pore fluids are simultaneously compressed. The velocity of the Compressional Wave in the rock matrix is related to the mineral frame and the cementation between the grains, while the velocity of the slower component of the Compressional Wave that travels through the interconnected fluid path is determined by the physical properties of the pore fluids and the tortuosity of the connected pores in the rock.
In the published literature, the Compressional Wave that travels through the fluids in the interconnected pores is identified as Slow-Wave. Slow-Wave has been measured under laboratory conditions in samples of glass beads and different porous and permeable sandstones. The Slow-Wave travels at the fluid compressional velocity but over a longer distance along the tortuous interconnected pores between the two ends of the reservoir formation, which is being measured.
The Slow-Wave is diffusive and highly attenuated. For this reason, it has been difficult to measure the Slow-Wave in-situ in the reservoir rocks. The measurements related to the Slow-Wave provide a unique opportunity to determine the reservoir rock properties such as permeability and tortuosity, which affect the flow mechanism of the reservoir fluids. Since Slow-Wave cannot be measured due to its high attenuation in-situ in the sedimentary rocks of the reservoir, a new method of measuring Slow-Wave has been developed and described in this Patent.
Permeable rocks are elastically nonlinear due to: a) their morphology; b) the microstructures of their pores; c) the pore interconnections; and d) pore fluids. In a permeable rock that is elastically nonlinear, the interactions between two elastic waves can be used in a unique way to map its physical properties. An elastic wave generated within a rock can be made to interfere with an externally generated seismic signal, and their elastic nonlinear interaction can be measured to determine the bulk tortuosity and permeability of a reservoir formation.
When the Primary external signal is a sinusoidal wave of a predetermined frequency and time duration, it creates a moving wave of compressional and rarefaction fronts that are repetitive and travel one wavelength apart. Each compressional front is separated from the next compressional front by a wavelength. Due to the physical coupling between the rock matrix and the fluid-filled pores, a Drag-Wave is generated as the Primary Sinusoidal Wave propagates through the rock matrix. The Drag-Wave propagates through the fluid-filled interconnected pores at the same velocity as the Slow-Wave. This velocity depends on the pore fluid properties and the tortuous path of the pore interconnections.
The Primary Sinusoidal Wave and the Drag-Wave propagate through the rock simultaneously and they elastically interact with each other. Due to the elastic nonlinearity of the permeable rock, the interaction between these two waves can be detected and measured as the elastic nonlinear interaction of the high-frequency Primary-Wave and the low-frequency Drag-Wave.
When two elastically linear seismic waves travel together in a subsurface formation, the principle of superposition holds and there is no interaction between the two waves. However, when they travel through a formation that is elastically nonlinear, then a nonlinear interaction between the two elastic waves occurs, and summed and differenced frequencies are generated.
In a permeable subsurface formation that is nonlinear, the interaction between the high-frequency Primary-Wave and the low-frequency Drag-Wave generates the summed and differenced frequencies of the two seismic signals. These summed and differenced frequencies appear as the side lobes of the Primary-Wave spectrum, and can be measured. The measured values provide us with information that directly translates into the frequency content of the Drag-Wave. Measurement of the Drag-Wave frequency and its relative amplitude is directly related to the bulk tortuosity and bulk permeability of the reservoir formation.
Since the Drag-Wave is generated by the liquid/solid coupled motion of the Primary-Wave, its frequency is determined by the Primary-Wave frequency, the velocity of the Primary-Wave, and the velocity of the Drag-Wave. The velocity of the Primary-Wave can be determined by the first seismic arrivals of the crosswell seismic data; it is a standard practice and well known in the current art. The frequency of the Primary-Wave is the frequency of the input signal transmitted by the downhole source, in this case a predetermined sinusoidal signal. The frequency of the Drag-Wave can be measured from the display of the side lobes of the frequency spectrum, since they result from summing and differencing of the Primary-Wave frequency and the Drag-Wave frequency. The velocity of the Drag-Wave can be calculated by:
Fdrag/F=Vdrag/(Vxe2x88x92Vdrag)
where Fdrag is the frequency of the Drag-Wave; F is the frequency of the Primary-Wave; Vdrag is the velocity of the Drag-Wave; and V is the velocity of the Primary-Wave.
The Drag-Wave velocity and the Slow-Wave velocity are the same, since the Drag-Wave is a form of Slow-Wave that is generated as the Primary-Wave propagates through a reservoir formation, due to the coupling between the rock matrix and the pore fluids. For this invention, the Drag-Wave nomenclature has been used since there is some confusion with the true meaning of xe2x80x9cSlow-Wavexe2x80x9d in the way it has been used by different authors in the published literature.
Once the Drag-Wave velocity is known, the bulk tortuosity of the reservoir formation between two wells can be calculated as:
Vdrag=Vfluid/T
where T is Tortuosity; and Vfluid is the compressional velocity in the pore fluid. Tortuosity is a measure of the sinuosity of the pores. Once the Tortuosity of the permeable formation has been determined, the Sinuosity of the interconnected pores can be calculated. Velocity of the pore fluids in the reservoir rocks can be measured by using the well-known Time-Average equation developed by Wyllie et al (1958). This equation is often used to relate the velocity of the reservoir formation and the porosity.
1/Formation velocity=Porosity/Pore Fluid Velocity+(1xe2x88x92Porosity)/Velocity of Rock Matrix.
Different wireline well logs are run as a normal routine, to identify the rocks, evaluate the reservoir formations, and to measure their petrophysical and elastic properties. The reservoir formation velocity is routinely measured using wireline Sonic Logs. In addition to the well logs coring of the reservoir formations is carried out for detailed analysis. The core of the reservoir rock is the only direct source of data for a particular reservoir. Oil and Gas exploration industry uses well logs and core evaluation as a general practice for reservoir characterization. Reservoir characterization instruments and coring tools are readily available in the industry to measure the elastic and petrophysical properties of the reservoir rocks and to obtain samples of the reservoir fluids.
Core Measurements provide an accurate value of the velocity of the rock matrix and the porosity of the reservoir rock. The industry has the equipment and knowledge for the measurements of the acoustic velocity of a core sample under a wide range of pore and confining pressures. Measurements can be made either with dry or saturated core samples. The texture of the core is analyzed to determine the train size, shape, and distribution. Porosity and crack density is measured. Once the reservoir formation velocity is known from the Sonic Log, and Velocity of the rock Matrix and Porosity is measured using the core sample, the velocity of the Pore Fluid can be calculated, using the Time-Average equation described above. In the case, where the samples of the reservoir fluids are available, direct measurements of the reservoir fluid properties can be made. The Modulation Formation Tester (Schlumberger) tool provides formation and hydrostatic pressure, temperature and fluid resistivity while fluid sample is being acquired. There are similar tools available from other service companies. The recovery of in situ pore fluid provides samples, which can be used to analyze the pore fluid properties. The velocity of the pore fluid can be measured as a part of the analysis. The velocity derived from in situ pore fluid measurements can be used to calibrate the velocity derived using Time-Average equation.
The Tortuosity xe2x80x98Txe2x80x99 equals to:
T=(La/L)2
where La is the actual (sinuous) length of the interconnected pores in a formation of length L.
So we can simplify the equation for Vdrag:
Vdrag=Vfluid(L/La)
Basically, this equation says that the Drag-Wave travels at the fluid compressional velocity, but over the longer distance along the tortuous interconnected pores between two end points of a reservoir formation (between two wells).
Scheidegger (1960) showed that permeability of a solid that has porosity xe2x80x98"PHgr"xe2x80x99 containing sinuous pores of constant radius xe2x80x98rxe2x80x99 and tortuosity xe2x80x98Txe2x80x99 is given by:
K="PHgr"r2/8T
where xe2x80x98Kxe2x80x99 is the permeability of the rock. Once the bulk tortuosity of a reservoir formation has been determined, the bulk permeability can be calculated. The permeability is strongly dependent on pore size, and is also a function of the rock tortuosity.
The amplitude of the summed and differenced frequencies of the two seismic waves, which are created due to the nonlinear elastic interaction in a permeable rock, is directly related to the product of the amplitudes of the two waves. So, the relative amplitude of the frequency side lobes created due to the interaction between the Primary-Wave and the Drag-Wave gives us a measure of the relative amplitude of the Drag-Wave, since the Primary-Wave input signal is known. Knowing the relative amplitude of the Drag-Wave between different well pairs, and by keeping the input signal at a constant level, we are able to determine a qualitative measure of the rock properties of the reservoir formation between one well pair to the next well pair. The amplitude of the Drag-Wave is related to the transfer of energy from the Compressional Wave to the pore fluids. This transfer of energy is more efficient if the pores are flat rather than circular. The amplitude of the Drag-Wave is also related to the width and size of the interconnections between the pores; it is a qualitative measure of the bulk permeability of the rock formation between the two wells.
The other useful information that is derived from the spectral analysis of the received and recorded signal is the presence and the relative amplitudes of the second and third harmonics of the fundamental frequency. The second and third harmonics are indicative of the elastic nonlinearity of the rock formation between the two wells. Rocks are elastically nonlinear due to structural defects in their matrix or frame caused by micro-fracturing, porosity, permeability and fluid saturation. The presence of harmonics, along with the frequency side lobes created by the presence of Drag-Wave, is a further confirmation of permeability of a rock formation between the two wells.
Based on experience in operating and producing from a particular reservoir, a geologic model of the reservoir is already in place. This geologic model can be calibrated against the new information that is added in the form of relative amplitudes of the Drag-Wave and the relative nonlinearity of the reservoir rock between different well pairs.
This invention outlines a new concept of measuring in-situ the velocity of the Slow Compressional Wave (Drag-Wave), and the bulk tortuosity of a permeable reservoir formation. Absence of the Drag-Wave between any two sampled depths in the source and receiver wells indicates that between those two levels there is no straight-line permeable connection between the two wells. The field implementation of this invention is relatively easy and requires standard crosswell seismic equipment, which is available and known in the industry. It is a standard practice to use a downhole source in one well and receiver arrays in adjacent wells. The current standard equipment can easily be adapted to transmit mono-frequency signals at discrete pre-selected frequencies and recordings made using multiple downhole receivers with independent outputs. Anyone familiar with crosswell seismic can plan and record the data needed to provide complete vertical coverage of the reservoir formations of interest to map permeability connections between the wells.
The crosswell seismic methods are well known in the industry, have been practiced for over ten years, and do not require a lot of description.